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On globally generated vector bundles on projective spaces. II. (English) Zbl 06244901
Summary: Extending the main result of J. C. Sierra and L. Ugaglia [J. Pure Appl. Algebra 213, No. 11, 2141–2146 (2009; Zbl 1166.14011)], we classify globally generated vector bundles on $$\mathbb P^n$$ with first Chern class equal to 3.

##### MSC:
 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
Full Text:
##### References:
 [1] C. Anghel, N. Manolache, Globally generated vector bundles on $$\mathbb{P}^n$$ with $$c_1 = 3$$, arXiv:1202.6261v1 [math.AG]. · Zbl 1279.14053 [2] E. Ballico, S. Huh, F. Malaspina, Globally generated vector bundles of rank 2 on a smooth quadric threefold, arXiv:1211.1100 [math.AG]. · Zbl 1281.14038 [3] E. Ballico, S. Huh, F. Malaspina, On higher rank globally generated vector bundles over a smooth quadric threefold, arXiv:1211.2593 [math.AG]. · Zbl 1350.14031 [4] E. Ballico, S. Huh, F. Malaspina, Reflexive and spanned sheaves on $$\mathbb{P}^3$$, arXiv:1301.1822 [math.AG]. · Zbl 1304.14023 [5] Chiodera, L.; Ellia, Ph., Rank two globally generated vector bundles with $$c_1 \leq 5$$, Rend. Istit. Mat. Univ. Trieste, 44, 413-422, (2012) · Zbl 1271.14020 [6] Ph. Ellia, Chern classes of rank two globally generated vector bundles on $$\mathbb{P}^2$$, arXiv:1111.5718 [math.AG]. [7] Fania, M. L.; Mezzetti, E., Vector spaces of skew-symmetric matrices of constant rank, Linear Algebra Appl., 434, 2383-2403, (2011) · Zbl 1215.15017 [8] Huh, S., On triple Veronese embeddings of $$\mathbb{P}^n$$ in the Grassmannians, Math. Nachr., 284, 1453-1461, (2011) · Zbl 1279.14014 [9] Manivel, L.; Mezzetti, E., On linear spaces of skew-symmetric matrices of constant rank, Manuscripta Math., 117, 319-331, (2005) · Zbl 1084.14050 [10] N. Manolache, Globally generated vector bundles on $$\mathbb{P}^3$$ with $$c_1 = 3$$, arXiv:1202.5988v1 [math.AG]. [11] Okonek, Ch.; Schneider, M.; Spindler, H., Vector bundles on complex projective spaces, (Progress in Mathematics, 3, (1980), Birkhäuser Boston, Mass) · Zbl 0438.32016 [12] Sierra, J. C.; Ugaglia, L., On globally generated vector bundles on projective spaces, J. Pure Appl. Algebra, 213, 2141-2146, (2009) · Zbl 1166.14011
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